Best Known (61−47, 61, s)-Nets in Base 5
(61−47, 61, 35)-Net over F5 — Constructive and digital
Digital (14, 61, 35)-net over F5, using
- net from sequence [i] based on digital (14, 34)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 3 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(61−47, 61, 39)-Net over F5 — Digital
Digital (14, 61, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
(61−47, 61, 102)-Net in Base 5 — Upper bound on s
There is no (14, 61, 103)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(561, 103, S5, 47), but
- the linear programming bound shows that M ≥ 4181 564648 455170 129201 793753 034978 682708 608421 726359 414523 092254 516167 809441 640201 839618 384838 104248 046875 / 918 660028 038993 797791 684674 926208 163709 559531 824032 778011 594611 > 561 [i]